Various and Sundry

The latest New Scientist has an article about Erik Verlinde’s “entropic gravity”, with enthusiastic remarks from Robbert Dijkgraaf and Stanley Deser. Gerard ‘t Hooft expresses pleasure at seeing a string theorist talking about “real physical concepts like mass and force, not just fancy abstract mathematics”. According to the article, the problem with Einstein’s General Relativity is that its “laws are only mathematical descriptions.” I guess a precise mathematical expression of a theory is somehow undesirable, much better to have a vague description in English about how it’s all due to some mysterious entropy. There’s even an editorial about this:

Now we could be closing in on an explanation of where gravity comes from: it might be an emergent property of the way objects are organised, much as fluidity arises as a property of water…. This idea might seem exotic now, but to kids of the future it might be as familiar as apples.

In a new preprint, Lee Smolin uses Verlinde’s work in a very different way, to show that Newton’s law of gravity must emerge from the microscopic quantum gravity approach Smolin favors, that of loop quantum gravity.

Also on the New Scientist/entropy front, there’s a review by Craig Callender of Sean Carroll’s new book. I’d been wondering what philosophers of science would have to say about the book, and the reaction to Carroll’s multiverse explanation of the arrow of time was about what I suspected it would be:

Daring to speculate in the absence of well-confirmed theory, Carroll jumps from clue to clue, from black hole physics to string theory to the holographic principle, until he arrives at his destination: an eternal “mother space-time” from which a multiverse of baby universes are continually bubbling up and pinching off. The mother space-time is a high entropy vacuum that gives birth to universes like our own, some of which we can expect to begin with low entropy. Problem solved, says Carroll, because that is natural.

Carroll seems slightly embarrassed by the many leaps of faith he asks of his reader in proposing this solution, and the prose of Part IV sometimes reads like the pitch of an honest used-car salesman: “This car is a dream! True, the tyres are bald, brakes unsound and transmission sticky, but you’ll love it!”

Carroll and other peddlers of multiverses make us an offer: we will explain the unexplained if you add vast unconfirmable matters of fact into your ontology. In this case that includes a host of disconnected baby universes, an eternal mother universe entirely unlike ours, and half a dozen unknown mechanisms to get all this working. Assuming this explains the low entropy past – and with so much unknown it is hard to be sure another conspiracy isn’t lurking within – is this a good deal?

In most cases I don’t think so. Why is Manchester United perennially a good soccer team? Surely most solutions of the laws of physics don’t have them winning so much. How unnatural (and unfair) those initial conditions are! Nonetheless, a frothy sea of baby universes tempts no one. We shrug and say, that’s just the way it is. Sometimes it is best not to scratch explanatory itches.

Witten now has a long preprint out about his beautiful recent work on analytic continuation of Chern-Simons theory that I wrote about here last fall.

My colleague Johan de Jong has been working for a few years now on what he calls the Stacks Project, which aims at a detailed, foundational exposition of the theory of algebraic stacks, beginning with the necessary algebraic geometry. He has structured this along the lines of an open source software project, encouraging contributions to the project from other algebraic geometers. The latest addition to the project is a blog.

A huge proportion of the mathematics research literature is now controlled by the publishing company Springer Science + Business Media. Last April there were reports that the owners of the business had it up for sale for about $2.9 billion. The CEO denied these reports, stating “We are not for sale, there is no truth in Springer being sold”. Last month came the announcement that Springer was being sold, to two private equity firms from Sweden and Singapore. The price was about $3.4 billion, with the new owners also taking on $2.9 billion of the company’s debt.

It’s not clear if there are any implications for mathematics publishing, with this perhaps just a transfer of control of the mathematics literature from one group of private equity firms to another.

describes efforts to link string theory to experimental physics and uses analogies that nonscientists can understand. How does Chopin’s Fantasie-Impromptu relate to quantum mechanics? What would it be like to fall into a black hole? Why is dancing a waltz similar to contemplating a string duality?

and

After reading this book, you’ll be able to draw your own conclusions about string theory.

The introduction is available here, and ends with this description of recent debates over string theory:

I don’t aim to settle any debates about string theory in this book, but I’ll go so far as to say that I think a lot of the disagreement is about points of view. When a noteworthy result comes out of string theory, a proponent of the theory might say, “That was fantastic! But it would be so much better if only we could do thus-and-such.” At the same time, a critic might say, “That was pathetic! if only they had done thus-and-such, i might be impressed.” in the end, the proponents and the critics (at least, the more serious and informed members of each camp) are not that far apart on matters of substance. everyone agrees that there are some deep mysteries in fundamental physics. nearly everyone agrees that string theorists have mounted serious attempts to solve them. And surely it can be agreed that much of string theory’s promise has yet to be delivered upon.

Yeah, that about does it for physics. All done. Math can pretty much take it from here.

Update: Robert Helling gives his take on the Verlinde paper here. It reminds him of a certain proof that reaches an unreasonable conclusion using the rules “time=money” and “money is the root of evil”. I noticed this via an arXiv trackback. Funny, for some reason there are no trackbacks to my postings on this topic

17 Responses to Various and Sundry

I get a sense that you are not so into the entropy/gravity connection, but I think it’s going to be a very fruitful area for mathematical General Relativity in the coming years. There have been about a dozen mathematical papers on the subject, most of them coming from the viewpoint of Perelman’s entropy functional, Ricci Flow and all those things. It may not be Perelman’s entropy functional, maybe a modified entropy functional, but this is one of the most mysterious areas in geometric analysis right now.

That piece about math software was really entertaining! I still have my working HP-71B from student days and still use my TI-92+ to do algebra in spacetime on the bus and train. I’m sort of surprised he never used Derive, which I find incredibly useful – a sort of LISP dialect that is specifically for math – the array processing is magnificent and better even than APL, and of course it handles the complex domain effortlessly.

I heartily endorse the SAGE project, which is both fun in itself and very useful as well.

Verlinde considers the change in entropy dS for displacements dx assuming a holographic principle. But in his calculation he implicitly assumes the geometry of a smooth and indeed flat geometry.

There is of course nothing wrong about that, but if Lee Smolin wants to use this argument, then he has to first show that there is a reasonable limit of loop quantum gravity, which reproduces this smooth and (almost) flat spacetime and I dont see that.

Peter is right to criticize that the entropic formulation by Jacobson and Verlinde is not deep, because describing space-time as a thermodynamic limit does not tell (almost) anything about the microscopic constituents.

When Bernoulli deduced the ideal gas law from atoms, he was able to show that gases are made of atoms whizzing around. But as suggested by many, almost any microscopic degree of freedom at Planck scale will give the proper thermodynamic limit: loops, ribbons, etc. all yield a limit that then leads to Jacobson’s and Verlinde’s argument.

It is highly probable that the Jacobson/Verlinde argument is not able to distinguish between different microscopic models of quantum gravity. There is one exception though: the argument eliminates all theories with higher dimensions. In my view, the only conclusion about new physics that can be drawn from the Jacobson/Verlinde argument is: space-time is emergent and is made of microscopic degrees of freedom that fluctuate in 3+1 dimension.

Quantum gravity people will say: we knew this since (at least) 15 years. And they are right. However, if the exploration of quantum gravity were the right path to find the microscopic degrees of freedom, they would have been found long ago. In fact, quantum gravity does not allow to deduce much about the microscopic degrees of freedom.

The paper by Verlinde does not change the situation at all. Except that it confirms that superstrings are not the right microscopic degrees of freedom, because they do not live in 3+1 dimensions. But Peter would not call this a new result 🙂

I think that Lubos is wrong. Unruh’s proportionality between acceleration and temperature implies that gravity can be seen as an thermal/entropic effect. There is little doubt about it. If you want to get rid about the gravity-entropy relation, you must get rid of Unruh radiation – and that is impossible.

On the other hand, this does not tell anything new, as I argued in my previous comment. The reason that Lubos is against the connection between gravity and entropy is clear: he understands that the Jacobson/Verlinde argument undermines string theory, because it excludes higher dimensions. Worse, through Verlinde’s simplification for Newtonian gravity, EVERY physicist now understands that higher dimensions are out! This is Lubos’ nightmare: a simple argument that suggests that string theory is wrong. Even worse, the argument is made by one of the world’s most distinguished string theorists! We can all guess what will happen: Lubos will start discrediting the argument with the same anger with which he discredits global warming. Watch the show.

Unfortunately, whenever I mention the Verlinde business, it’s all anyone seems to want to comment on. I get dozens of comments (most of which I delete) submitted by people who want to discuss their own ideas about how the fundamental problems of physics can be solved using simple ideas from thermodynamics and high school math. Moderating these comments depresses me, so please stop doing it. Unless you have something really new, interesting, and very directly related to the Verlinde story, please don’t post comments on the subject here.

Frank, which part of Verlinde’s argument singles out 3+1 dimensions? I have just been going through the early parts of the paper to try to get a better feel for his argument, and no part of it seems to depend on the dimensionality of spacetime.

I don’t see any disagreement with most serious string theorists about whether string theory now gives a viable unified theory (it doesn’t). Where we disagree is on the question of whether to be optimistic or pessimistic about prospects for the future of this idea. I haven’t seen anything in recent years that changes my pessimistic take on the situation, and I think even the more optimistic string theorists would agree that nothing learned recently adds to the case for optimism. Other than a small number of people who believe the landscape is serious physics, the majority of string theorists recognize that it’s a disastrous end-point for the idea of unification via string theory.

From your comment you misunderstand the argument I make. I begin the conclusions by saying: “It is important to emphasize that I have not shown here that classical spacetime emerges from loop quantum gravity, as we have assumed that there is a classical spacetime in the exterior region where we make measurements. What has been shown is that if there is a classical spacetime that emerges then Newton’s law of gravity is necessarily satisﬁed. ” Perhaps you will find the actual argument, which is to that limited conclusion, more convincing.

Rhys, the whole Verlinde argument only works in 3d. There are many ways to see this. One is to check Jacobson’s original argument, which only works in 3d; another is to recall the relation between 3d and the “square” in 1/r^2.

As I predicted, Motl is fighting with all his energy. Now Verlinde is already a “crackpot”. It seems that this attitude is shared by many. (It makes Jacobson a crackpot as well.) I can only shake my head in dismay. Even Seiberg, some time ago, has written a long paper on emergent space-time. It is now obvious since 15 years that space and gravity are due to some microscopic degrees of freedom, and now that there is a simple argument to show this, many dismiss it.

Wheeler spoke of “space-time foam” long ago. Then came the string theorists, and they replaced foam by compactified 11d space. But they were wrong. Wheeler was right. That is the simple truth. Space-time foam exists, and its thermodynamics produces gravity. Space-time is not a compactified 11d space.

Sorry, but I’m with Lubos on this, and I don’t believe your argument that this only works in 4d. You can hope (as Seiberg does) to get space-time to “emerge” from a higher dimensional string theory, or from “space-time foam”, from bits, from all sorts of things, with all sorts of different possible dimensions “emerging” at different distance scales. But by assuming just thermodynamics + some version of holography, you are starting with almost zero input. From this you will get almost zero output, not stringent limitations on the nature of the fundamental theory, for instance on its dimensionality.